Extension of unbounded uniformly continuous functions and pseudometrics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10492945" target="_blank" >RIV/00216208:11320/24:10492945 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Xe.6McvG1P" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Xe.6McvG1P</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.topol.2024.108959" target="_blank" >10.1016/j.topol.2024.108959</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extension of unbounded uniformly continuous functions and pseudometrics

Popis výsledku v původním jazyce

In this paper we aim to characterize uniformly continuous real functions and pseudometrics on metric spaces, having uniformly continuous extension. For functions we use a very similar approach as McShane in [7] using moduli of continuity. By doing that we obtain an explicit formula for the extension. We also show that our characterization for functions is equivalent to one proposed in [8] for uniform spaces. We then show that a similar approach can be done for uniformly continuous pseudometrics. To do so we use the notion of chainable metric spaces and intrinsic metrics defined in [9]. A somewhat similar approach has been studied in [6] for normed linear spaces. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Název v anglickém jazyce

Extension of unbounded uniformly continuous functions and pseudometrics

Popis výsledku anglicky

In this paper we aim to characterize uniformly continuous real functions and pseudometrics on metric spaces, having uniformly continuous extension. For functions we use a very similar approach as McShane in [7] using moduli of continuity. By doing that we obtain an explicit formula for the extension. We also show that our characterization for functions is equivalent to one proposed in [8] for uniform spaces. We then show that a similar approach can be done for uniformly continuous pseudometrics. To do so we use the notion of chainable metric spaces and intrinsic metrics defined in [9]. A somewhat similar approach has been studied in [6] for normed linear spaces. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Topology and its Applications

ISSN

0166-8641

e-ISSN

1879-3207

Svazek periodika

353

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

108959

Kód UT WoS článku

001255621100001

EID výsledku v databázi Scopus

2-s2.0-85195028587